278 NOTE ON THE FORMULA FOE THE GRADIENT WIND [389
giving the velocity v in terms of the barometric gradient dp/da by means of a quadratic. As is evident from the case w = 0, the positive sign in the alternative is to be taken when x and r are drawn in opposite directions.
In (7) r is not derivable from the barometric chart, nor can -^ be determined strictly by means of p. But in many cases it appears that the more important part of p, at any rate in moderate latitudes, is that which depends upon (o, so that approximately from (5)
(8)
Substituting this value of ty in the smaller terms, we get as a second approximation
With like approximation we may identify r in (7) with the radius of curvature of the isobaric curve which passes through the point in question.
The interest of these formulae depends largely upon the fact that the velocity calculated as above from the barometric gradient represents fairly well the wind actually found at a moderate elevation. At the surface the discrepancy is larger, especially over the land, owing doubtless to friction.f the relative motion,